Multiple (mathematics)
From Wikipedia, the free encyclopedia
In mathematics, a multiple of an integer is the product of that integer with another integer. In other words, for integer a, b is a multiple of a if b = na for some integer n. If a is not zero, this is equivalent to saying that b / a is an integer.
[edit] Examples
14, 49 , -21 and 0 are multiples of 7 whereas 3 and -6 are not. This is because there are integers that 7 may be multiplied by to reach the values of 14, 49, 0, and -21, while there are no such integers for 3 and -6. Each of the products listed below, and in particular, the products for 3 and -6, is the only way that the relevant number can be written as a product of 7 and another real number:
;
;
;
;
, and 3 / 7 is a fraction, not an integer;
, and − 6 / 7 is a fraction, not an integer.
[edit] Properties
- 0 is a multiple of everything (
). - The product of any integer n and any integer is a multiple of n. In particular, n, which is equal to
, is a multiple of n (every integer is a multiple of itself), since 1 is an integer. - If a and b are multiples of x, then a + b, a − b, (p − 1)! + 1 is a multiple of p.
